Learning Maxwell pendulum motion.

 

Accessories: installation - Maxwell pendulum the FPM - 03.

 

Objective: Familiarization with the complex motion of a solid body by the example of Maxwell's pendulum movement.

 

Fitting Description

Pendulum FPM Maxwell - 03.

 

General view of the FPM Maxwell pendulum - 03 is shown in Figure 4.1.

The base (1) is equipped with adjustable feet (2), which allows to align the instrument. At the base of fixed column (3), to which is attached a fixed upper bracket (4) and a movable lower bracket (5). The upper arm is an electromagnet (6), a photoelectric sensor №1 (7) and the knob (8) for fastening and adjusting the length of the bifilar suspension pendulum.

Bottom bracket with attached thereto a photoelectric sensor №2 (9) can be moved along the column and fixed in an arbitrary position of favorites.

A pendulum (10) of the device - a roller mounted on an axle and bifilar manner superimposed on the various rings (11), thereby making different, the moment of inertia.

Pendulums overlaid ring is held in an upper position by an electromagnet. The length of the pendulum is determined on the millimeter scale on the device column.

unok 4.1

Theoretical introduction

With the release of the pendulum, he starts to move steadily downward and rotating around its axis of symmetry.

Rotation, continuing to lower inertia of the movement (when the thread already unwound), again leads to the filament winding on the rod, and hence to the rise of the pendulum. The movement of the pendulum then slows down, the pendulum stops and re-starts its downward movement, etc.

 

The equation of motion of the pendulum without considering friction forces are of the form:

M=mg-2T (1)

Ie=2Tr (2)

a=er (3)

where: m - mass of the pendulum; I is the moment of inertia of the pendulum; g - acceleration due to gravity; r is the radius of the rod; T - the thread tension (a); a - acceleration of translational motion of the center of mass of the pendulum;; e - - angular acceleration.

The acceleration may be obtained from the measured travel time t and the distance traveled by the pendulum, h of the equation assuming that the uniformly accelerated motion forward:

(4)

Equations (1) - (3) gives:

2Т=m(g-a) (5)

(6)

Substituting (6) (5), we obtain:

(7)

or taking into account (4) finally will have:

(8)

where: I - moment of inertia of the pendulum in kg.m2

D=D₀ + D_n D_n = 0.5 mm = 0,00005m

D - outside diameter of the pendulum axis in position with a thread wound thereon suspension in m; D - is measured with calipers; t - time to fall in; g-gravitational acceleration in m / s ²; h - the length of the pendulum, which is equal to the height to which it rises in m; m - mass of the pendulum in place with a ring in kg, is calculated as follows:

m=m ₁+m ₂+m ₃ (9)

where: m ₁ - mass of the pendulum axle in kg; m ₂ - roller mass in kg;

m ₃ - weight imposed on the ring roller in kg.

 

Order of work

The device is ready for operation immediately after switching on the voltage and the light does not need heating.

You need:

1. Measure the height h of the pendulum.

2. Squeeze the button "Start" GRM-15 millisekundomera.

3. Wind up on the pendulum axle suspension thread, paying attention to the fact that it wound evenly, one coil to another.

4. Fix the pendulum by an electromagnet, paying attention to the fact that the thread in this position was not too flat.

5. tuck the pendulum in the position of its movement through an angle of 5 and release.

6. Read the measured value of the fall of the pendulum.

7. Press the "Reset".

8. Press the "Start".

9. Repeat steps 3-6.

10. Experiments repeat 5-7 times.

11. Determine the average time of fall of the pendulum

12. Using the expressions (8) and (9), the moment of inertia of the pendulum to count.

13. Calculate the theoretical value of the moment of inertia of the pendulum

I=+I₀+I_p+I_d (11)

where: ; and D-outer diameter of the pendulum axis;

where: D_p - the outer diameter of the roller,

where: D_d - the external diameter of the ring.

To measure D_p and D_d is necessary to remove the ring from the roller. Weight, mp md set.

14. Calculate the relative deviation of the experimentally determined value of the moment of inertia of the theoretical

(12)

where: I-moment of inertia obtained from the experiment using the formulas (8) and (9). IT- moment of inertia calculated from the formula (11)

15. Rate error in determining the moment of inertia based on the experimental data, appearing in the expression (8). All measurements must be made with great caution, as the pendulum can be easily damaged. It is necessary to protect the pendulum from the blows.

 

Control questions

1. In what part of Maxwell pendulum movements?

2. How the experimentally determined moment of inertia of the pendulum?

3. How to calculate theoretically the moment of inertia of the pendulum?

4. What are the moments of inertia units SI?

5. What is the angular acceleration?

6. In what units is measured by the angular acceleration?

7. In what units is measured by linear acceleration?

8. What is the relationship between the linear and angular accelerations?

9. As recorded 2nd Newton's law for rotary motion?

10. Record the forces acting on the pendulum Maxwell.

 

Literature

1. Savelyev IV The general course of physics. A.: Science, 1977, volume 1.

2. Frisch SE, AV Timoreva General Physics Course Volume 1, A.: Mektep 1971.

3. DV sivukhin The general course of physics. Vol.1, M.: Nauka, 1979.

 

Job number 5